Dressing a Naked Singularity: an Example

TL;DR

This paper demonstrates how a collapsing perfect fluid with self-similarity can transform an initial naked singularity into a black hole by forming an event horizon, using a specific self-similar solution and matching it to Schwarzschild spacetime.

Contribution

It provides a specific example of how naked singularities can be hidden behind horizons through matter collapse with self-similarity of the second kind.

Findings

Naked singularity can be trapped by an event horizon during collapse.

The solution involves a perfect fluid with self-similarity parameter α = -3.

The spacetime is matched to Schwarzschild spacetime, fulfilling energy conditions.

Abstract

Considering the evolution of a perfect fluid with self-similarity of the second kind, we have found that an initial naked singularity can be trapped by an event horizon due to collapsing matter. The fluid moves along time-like geodesics with a self-similar parameter $\alpha = -3$. Since the metric obtained is not asymptotically flat, we match the spacetime of the fluid with a Schwarzschild spacetime. All the energy conditions are fulfilled until the naked singularity.